文献类型：会议论文

英文题名：Unstable Manifold of Henon Map

作者：Chen Bo[1];Jia Meng

第一作者：陈波

通讯作者：Chen, B[1]

机构：[1]Xinxiang Univ, Dept Elect Engn, Xinxiang 453000, Peoples R China

第一机构：新乡学院机电工程学院

通讯机构：[1]corresponding author), Xinxiang Univ, Dept Elect Engn, Xinxiang 453000, Peoples R China.|[1107111]新乡学院机电工程学院;[11071]新乡学院;

会议论文集：International Conference on Advanced Materials Design and Mechanics (ICAMDM 2012)

会议日期：JUN 05-07, 2012

会议地点：Xiamen, PEOPLES R CHINA

语种：英文

外文关键词：discrete dynamical system; hyperbolic fixed point; unstable manifold

摘要：A new algorithm is presented for computing one dimensional unstable manifold of a map and Henon map is taken as an example to test the performance of the algorithm. The unstable manifold is grown with new point added at each step and the distance between consecutive points is adjusted according to the local curvature. It is proved that the gradient of the manifold at the new point can be predicted by the known points on the manifold and in this way the preimage of the new point could be located immediately. During the simulation, it is found that the unstable manifold of Henon map coincides with its direct iteration when canonical parameters are chosen which means order is obtained out of chaos. In the other several groups of parameters the two branches of the unstable manifolds are nearly symmetric, and they serve as the borderline of the Henon map iteration sequence. We hope that this would contribute to the further exploration of Henon map.